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Koszul-like algebras and modules

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Abstract

In this paper, the notion of Koszul-like algebra is introduced; this notion generalizes the notion of Koszul algebra and includes some Artin-Schelter regular algebras of global dimension 5 as special examples. Basic properties of Koszul-like modules are discussed. In particular, some necessary and sufficient conditions for KL(A) = L(A) are provided, where KL(A) and L(A) denote the categories of Koszul-like modules and modules with linear presentations (see [1]–[3], etc.) respectively, and A is a Koszul-like algebra. We construct new Koszul-like algebras from the known ones by the “one-point extension.” Some criteria for a graded algebra to be Koszul-like are provided. Finally, we construct many classical Koszul objects from the given Koszul-like objects.

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Authors and Affiliations

  1. Zhejiang Normal University, Jinhua, China

    Jia-Feng Lü

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  1. Jia-Feng Lü
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Correspondence to Jia-Feng Lü.

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Published in Russian in Matematicheskie Zametki, 2013, Vol. 93, No. 3, pp. 413–435.

The text was submitted by the author in English.

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Lü, JF. Koszul-like algebras and modules. Math Notes 93, 431–450 (2013). https://doi.org/10.1134/S0001434613030103

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  • DOI: https://doi.org/10.1134/S0001434613030103

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